Question

What is the quotient when you divide −2 3/5 by 4/5?(1 point)
Responses

−314
3 Start Fraction 1 over 4 End Fraction

−234
negative 2 Start Fraction 2 over 25 End Fraction

−2552
negative Start Fraction 25 over 52 End Fraction

413

Answer 1

To find the quotient of \(-2 \frac{3}{5}\) divided by \(\frac{4}{5}\), we first need to convert the mixed number \(-2 \frac{3}{5}\) into an improper fraction.

1. Convert \(-2 \frac{3}{5}\):
\[
-2 \frac{3}{5} = -\left(2 \times 5 + 3\right)/5 = -\left(10 + 3\right)/5 = -\frac{13}{5}
\]

2. Now, we need to divide \(-\frac{13}{5}\) by \(\frac{4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal:
\[
-\frac{13}{5} \div \frac{4}{5} = -\frac{13}{5} \times \frac{5}{4}
\]

3. Simplifying this gives:
\[
-\frac{13 \times 5}{5 \times 4} = -\frac{13}{4}
\]

Thus, the quotient of \(-2 \frac{3}{5}\) divided by \(\frac{4}{5}\) is \(-\frac{13}{4}\).

Since the options listed do not appear to match this directly, let's check to see if it can be expressed differently:

\(-\frac{13}{4}\) can be converted to a mixed number:
\[
-\frac{13}{4} = -3 \frac{1}{4}
\]

Thus, the quotient is \(-3\frac{1}{4}\).

The correct response is:
**−3 Start Fraction 1 over 4 End Fraction**.